As discussed in [1]}, \(\Vert {H}^{+}-\hat{{H}}^{+}\Vert ,\mathbb {E}\Vert {L}-\hat{{L}}\Vert \)  are perturbation terms that can be bounded in terms of \(\Vert {G}-\hat{{G}}\Vert \) 
via Lemma REF  and Lemma REF . Theorem REF  shows that the stochastic Ho-Kalman Algorithm has the same error bounds as its deterministic counterpart, which says the estimation errors for system matrix decrease as fast as \(O(\frac{1}{N^{1/4}}).\)  Our analysis framework can be easily extended to achieve the optimal error bounds \(O(\frac{1}{\sqrt{N}})\)  mentioned in [2]}, [3]}, [4]}, [5]}.
